Nothing softens the sting of being fired from the Los Angeles Lakers organization like a chicken sandwich ... just ask ex-coach Mike Brown ... who hit up a Chick-fil-A right after he got the chop today.

TMZ obtained photos of Brown hanging at a Chick-fil-A restaurant in Costa Mesa, CA around 11:30 AM ... just a few hours after news broke that he was fired from the team over their dismal 1-4 start.

We're told Brown was super-nice to fans ... taking pics and shaking hands ... but he never discussed the firing.

However, it appears Brown WAS in the mood to talk ... 'cause he was in the middle of a phone convo with legendary L.A. sports reporter Jim Hill when he stopped to take the above photo.

Brown seems to be handling the situation with class -- releasing a statement saying, "I have great respect for the Buss family and the Lakers’ storied tradition and I thank them for the opportunity they afforded me."